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Discrete Mathematics by Babu Ram

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4

Logic

Logic is the study of reasoning and is specifically concerned with whether a particular reasoning is valid. It is a science of the necessary laws of thought, without which no employment of the understanding and the reason takes place.

4.1 PROPOSITIONS

Definition 4.1

A declarative sentence that is either true or false, but not both is called a Proposition or a Statement.

EXAMPLE 4.1

Which of the following are propositions?

  1. London is the capital of France
  2. Open the door
  3. Take two tablets of medicine
  4. x + y > 0, x, yZ
  5. The only positive integers that divide a prime number are 1 and the number itself.
  6. The sun is hot

Solution.

  1. The sentence is declarative and false. Hence, it is a proposition.
  2. The sentence “Open the door” is not declarative. ...

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